LONDON — In a sign of deepening crisis in the Church of England after it rejected the appointment of women as bishops, its spiritual leader said Wednesday that the church had ‘‘undoubtedly lost a measure of credibility’’ and had a ‘‘lot of explaining to do’’ to people who found its deliberations opaque.

The archbishop of Canterbury, the Most Rev. Rowan Williams, was speaking after an emergency meeting of bishops called to debate Tuesday’s narrow balloting by its General Synod rejecting the ordination of women as bishops, even though female priests account for a third of the Church of England’s clergy members. Female priests hold senior positions like canon and archdeacon, and some had hoped to secure appointments as bishops by 2014.

The vote represented a direct rebuff to Williams’s reformist efforts during his 10 years as head of the church and a huge setback to a campaign for change that has been debated intensely for the past decade.

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More than 70 percent of the 446 synod votes Tuesday were in favor of opening the church’s episcopacy to women. But the synod’s voting procedures require a two-thirds majority in each of its three ‘‘houses’’: bishops, clergy, and laity. The bishops approved the change by 44-3, and the clergy by 148-45. The vote among the laity, though, was 132-74, six votes less than the two-thirds needed.

Some British lawmakers suggested Wednesday that the vote would create a crisis of church-state relations, since the rejection of female bishops contradicts national laws on gender equality.